Question

A palace has seven gates. At every gate, a guard takes half the number of apples you have and returns one back to you. What should be the initial number of apples you need to carry to be left with exactly two apples after you pass all seven gates?

Option 1: 5 apples
Option 2: 7 apples
Option 3: 18 apples
Option 4: 63 apples

Answer 1

The person would need to carry 510 apples initially to be left with exactly two after passing through all seven gates. This is achieved by reversing the process and doubling the total at each gate after returning one apple.

Step-by-step explanation:

You're asking about a problem that involves a simple yet tricky mathematical concept. To be left with exactly two apples after you pass all seven gates, you need to reverse the process. Starting with two apples and moving backwards, at each gate you subtract one (the apple you received back) and then double your current number of apples. Let's do this backward calculation step by step:

1. Before the 7th gate, you have ((2+1)*2)=6 apples.
2. Before the 6th gate, you have ((6+1)*2)=14 apples.
3. Before the 5th gate, you have ((14+1)*2)=30 apples.
4. Before the 4th gate, you have ((30+1)*2)=62 apples.
5. Before the 3rd gate, you have ((62+1)*2)=126 apples.
6. Before the 2nd gate, you have ((126+1)*2)=254 apples.
7. Before the 1st gate, you have ((254+1)*2)=510 apples.

Therefore, you would need to start with 510 apples initially to have exactly two apples left after passing through all seven gates of the palace.

Learn more about Number Problem